### Abstract

We present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms which use polar representation. The main advantage of using a polar representation is that it allows us to exert independent control over grid size and bend positions. Polar coordinates allow us to specify different vertex resolution, bend-point resolution and edge separation. We first describe a standard (Cartesian) representation algorithm (CRA) which we then modify to obtain a polar representation algorithm (PRA). In both algorithms we are concerned with the following drawing criteria: angular resolution, bends per edge, vertex resolution, bend-point resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, √2/2 edge separation, 5n × 5n/2 drawing area and 1/2d(v) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of φ/4d(v) 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point resolution and edge separation are parameters that can be modified to achieve different types of drawings and drawing areas. In particular, for the same parameters as the CRA algorithm (unit bend-point resolution and √2/2 edge separation), the PRA algorithm creates a drawing of size 9n × 9n/2.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 407-421 |

Number of pages | 15 |

Volume | 2265 LNCS |

State | Published - 2002 |

Event | 9th International Symposium on Graph Drawing, GD 2001 - Vienna, Austria Duration: Sep 23 2001 → Sep 26 2001 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2265 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 9th International Symposium on Graph Drawing, GD 2001 |
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Country | Austria |

City | Vienna |

Period | 9/23/01 → 9/26/01 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 2265 LNCS, pp. 407-421). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2265 LNCS).

**Polar coordinate drawing of planar graphs with good angular resolution.** / Duncan, Christian A.; Kobourov, Stephen G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 2265 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2265 LNCS, pp. 407-421, 9th International Symposium on Graph Drawing, GD 2001, Vienna, Austria, 9/23/01.

}

TY - GEN

T1 - Polar coordinate drawing of planar graphs with good angular resolution

AU - Duncan, Christian A.

AU - Kobourov, Stephen G

PY - 2002

Y1 - 2002

N2 - We present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms which use polar representation. The main advantage of using a polar representation is that it allows us to exert independent control over grid size and bend positions. Polar coordinates allow us to specify different vertex resolution, bend-point resolution and edge separation. We first describe a standard (Cartesian) representation algorithm (CRA) which we then modify to obtain a polar representation algorithm (PRA). In both algorithms we are concerned with the following drawing criteria: angular resolution, bends per edge, vertex resolution, bend-point resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, √2/2 edge separation, 5n × 5n/2 drawing area and 1/2d(v) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of φ/4d(v) 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point resolution and edge separation are parameters that can be modified to achieve different types of drawings and drawing areas. In particular, for the same parameters as the CRA algorithm (unit bend-point resolution and √2/2 edge separation), the PRA algorithm creates a drawing of size 9n × 9n/2.

AB - We present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms which use polar representation. The main advantage of using a polar representation is that it allows us to exert independent control over grid size and bend positions. Polar coordinates allow us to specify different vertex resolution, bend-point resolution and edge separation. We first describe a standard (Cartesian) representation algorithm (CRA) which we then modify to obtain a polar representation algorithm (PRA). In both algorithms we are concerned with the following drawing criteria: angular resolution, bends per edge, vertex resolution, bend-point resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, √2/2 edge separation, 5n × 5n/2 drawing area and 1/2d(v) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of φ/4d(v) 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point resolution and edge separation are parameters that can be modified to achieve different types of drawings and drawing areas. In particular, for the same parameters as the CRA algorithm (unit bend-point resolution and √2/2 edge separation), the PRA algorithm creates a drawing of size 9n × 9n/2.

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UR - http://www.scopus.com/inward/citedby.url?scp=23044533409&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:23044533409

SN - 3540433090

SN - 9783540433095

VL - 2265 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 407

EP - 421

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -